arXiv subjects

Hanlin Sun

Publications and source records attributed to Hanlin Sun.

At least 19 recordsLinked to original sources

arXiv2026

Criticality and universality in network dismantling

Identifying the smallest set of elements whose removal dismantle a complex network, known as the network dismantling problem, is a fundamental task with many practical applications. Whereas network dismantling has been extensively studied over the past decade, most work has focused on developing efficient algorithms for large but finite networks. By contrast, the physics of the network dismantling process, namely how the network structural connectivity is affected by the removal of nodes or edges, remains largely unexplored in the thermodynamic limit. Here, we shed light on this understudied aspect of network dismantling by introducing an adaptive biased percolation process able to optimally dismantle a network. Through a systematic analysis of synthetic network models, we find that the proposed percolation process displays a universal phase transition, characterized by the abrupt and simultaneous disappearance of both the giant connected component and the largest 2-core, across networks with markedly different degree distributions. Simulations on real networks further support this universality, indicating that the physics of network dismantling is insensitive to a broad range of topological properties. Together, these results suggest that a topology-agnostic theory could be developed to explain the critical behavior of network dismantling.

physics.soc-ph↗

arXiv2026

Hackers or Hallucinators? A Comprehensive Analysis of LLM-Based Automated Penetration Testing

The rapid advancement of Large Language Models (LLMs) has created new opportunities for Automated Penetration Testing (AutoPT), spawning numerous frameworks aimed at achieving end-to-end autonomous attacks. However, despite the proliferation of related studies, existing research generally lacks systematic architectural analysis and large-scale empirical comparisons under a unified benchmark. Therefore, this paper presents the first Systematization of Knowledge (SoK) focusing on the architectural design and comprehensive empirical evaluation of current LLM-based AutoPT frameworks. At systematization level, we comprehensively review existing framework designs across six dimensions: agent architecture, agent plan, agent memory, agent execution, external knowledge, and benchmarks. At empirical level, we conduct large-scale experiments on 13 representative open-source AutoPT frameworks and 2 baseline frameworks utilizing a unified benchmark. The experiments consumed over 10 billion tokens in total and generated more than 1,500 execution logs, which were manually reviewed and analyzed over four months by a panel of more than 15 researchers with expertise in cybersecurity. By investigating the latest progress in this rapidly developing field, we provide researchers with a structured taxonomy to understand existing LLM-based AutoPT frameworks and a large-scale empirical benchmark, along with promising directions for future research.

cs.CR↗

arXiv2026

Enforcing Priority in Schedule-based User Equilibrium Transit Assignment

Denied boarding in congested transit systems induces queuing delays and departure-time shifts that can reshape passenger flows. Correctly modeling these responses in transit assignment hinges on the enforcement of two priority rules: continuance priority for onboard passengers and first-come-first-served (FCFS) boarding among waiting passengers. Existing schedule-based models typically enforce these rules through explicit dynamic loading and group-level expected costs, yet discrete vehicle runs can induce nontrivial within-group cost differences that undermine behavioral consistency. We revisit the implicit-priority framework of Nguyen et al. (2001), which, by encoding boarding priority through the notion of available capacity, characterizes route and departure choices based on realized personal (rather than group-averaged) travel experiences. However, the framework lacks an explicit mathematical formulation and exact computational methods for finding equilibria. Here, we derive an equivalent nonlinear complementarity problem (NCP) formulation and establish equilibrium existence under mild conditions. We also show that multiple equilibria may exist, including behaviorally questionable ones. To rule out these artifacts, we propose a refined arc-level NCP formulation that not only corresponds to a tighter, behaviorally consistent equilibrium concept but also is more computationally tractable. We reformulate the NCP as a continuously differentiable mathematical program with equilibrium constraints (MPEC) and propose two solution algorithms. Numerical studies on benchmark instances and a Hong Kong case study demonstrate that the model reproduces continuance priority and FCFS queuing and captures departure-time shifts driven by the competition for boarding priority.

cs.GT↗

arXiv2025

LLM-Guided Reinforcement Learning with Representative Agents for Traffic Modeling

Large language models (LLMs) are increasingly used as behavioral proxies for self-interested travelers in agent-based traffic models. Although more flexible and generalizable than conventional models, the practical use of these approaches remains limited by scalability due to the cost of calling one LLM for every traveler. Moreover, it has been found that LLM agents often make opaque choices and produce unstable day-to-day dynamics. To address these challenges, we propose to model each homogeneous traveler group facing the same decision context with a single representative LLM agent who behaves like the population's average, maintaining and updating a mixed strategy over routes that coincides with the group's aggregate flow proportions. Each day, the LLM reviews the travel experience and flags routes with positive reinforcement that they hope to use more often, and an interpretable update rule then converts this judgment into strategy adjustments using a tunable (progressively decaying) step size. The representative-agent design improves scalability, while the separation of reasoning from updating clarifies the decision logic while stabilizing learning. In classic traffic assignment settings, we find that the proposed approach converges rapidly to the user equilibrium. In richer settings with income heterogeneity, multi-criteria costs, and multi-modal choices, the generated dynamics remain stable and interpretable, reproducing plausible behavioral patterns well-documented in psychology and economics, for example, the decoy effect in toll versus non-toll road selection, and higher willingness-to-pay for convenience among higher-income travelers when choosing between driving, transit, and park-and-ride options.

cs.GT↗

arXiv2025

Triadic percolation on multilayer networks

Triadic interactions are special types of higher-order interactions that occur when regulator nodes modulate the interactions between other two or more nodes. In presence of triadic interactions, a percolation process occurring on a single-layer network becomes a fully-fledged dynamical system, characterized by period-doubling and a route to chaos. Here, we generalize the model to multilayer networks and name it as the multilayer triadic percolation (MTP) model. We find a much richer dynamical behavior of the MTP model than its single-layer counterpart. MTP displays a Neimark-Sacker bifurcation, leading to oscillations of arbitrarily large period or pseudo-periodic oscillations. Moreover, MTP admits period-two oscillations without negative regulatory interactions, whereas single-layer systems only display discontinuous hybrid transitions. This comprehensive model offers new insights on the importance of regulatory interactions in real-world systems such as brain networks, climate, and ecological systems.

nlin.AO↗

arXiv2025

Shortest-path percolation on scale-free networks

The shortest-path percolation (SPP) model aims at describing the consumption and eventual exhaustion of a network's resources. Starting from a network containing a macroscopic connected component, random pairs of nodes are sequentially selected, and if the length of the shortest path connecting the node pairs is smaller than a tunable budget parameter, then all edges along such a path are removed from the network. As edges are progressively removed, the network eventually breaks into multiple microscopic components, undergoing a percolation-like transition. It is known that SPP transition on Erd\H{o}s-R\'enyi networks (ERNs) belongs to same universality class as of the ordinary bond percolation if the budget parameter is finite; for unbounded budget, instead, the SPP transition becomes more abrupt than the ordinary percolation transition. By means of large-scale numerical simulations and finite-size scaling analysis, here we study the SPP transition on random scale-free networks (SFNs) characterized by power-law degree distributions. We find, in contrast with ordinary percolation, that the transition is identical to the one observed on ERNs, denoting independence from the degree exponent. Still, we distinguish finite- and infinite-budget SPP universality classes. Our findings follow from the fact that the SPP process drastically homogenizes the heterogeneous structure of SFNs before the SPP transition takes place.

physics.soc-ph↗

arXiv2024

Spatio-temporal activity patterns induced by triadic interactions in an in silico neural medium

Triadic interactions are general mechanisms by which a node or neuron can regulate directly the link or synapse between other two neurons. The regulation takes place in a familiar way by either depressing or facilitating synaptic transmission. Such interactions are ubiquitous in neural systems, accounting for axo-axonic synapses and tripartite synapses mediated by astrocytes, for instance, and have been related to neuronal and synaptic processes at different time-scales, including short and long-term synaptic plasticity. In the field of network science, triadic interactions have been shown to produce complex spatio-temporal patterns of connectivity. Here, we investigate the emergent behavior of an in silico neural medium constituted by a population of leaky integrate-and-fire neurons with triadic interactions. We observe that, depending on relevant parameters defining triadic interactions, different activity patterns emerge. These include i) a silent phase, ii) a low-activity phase in which complex spatio-temporal patterns of low neuronal firing rate emerge that propagate through the medium, iii) a high-activity phase characterized by complex spatio-temporal patterns of high neuronal firing rate that propagate through the neural medium as waves of high firing activity over a bulk of low activity neurons, and iv) a pseudo-blinking phase in which the neural medium switches between high and low activity states, in a similar fashion to up/down state transitions. Here we analyse in depth the features of such patterns and relate our findings to the recently proposed model of triadic percolation.

q-bio.NC↗

arXiv2024

Higher-order triadic percolation on random hypergraphs

In this work, we propose a comprehensive theoretical framework combining percolation theory with nonlinear dynamics in order to study hypergraphs with a time-varying giant component. We consider in particular hypergraphs with higher-order triadic interactions that can upregulate or downregulate the hyperedges. Triadic interactions are a general type of signed regulatory interaction that occurs when a third node regulates the interaction between two other nodes. For example, in brain networks, the glia can facilitate or inhibit synaptic interactions between neurons. However, the regulatory interactions may not only occur between regulator nodes and pairwise interactions but also between regulator nodes and higher-order interactions (hyperedges), leading to higher-order triadic interactions. For instance, in biochemical reaction networks, the enzymes regulate the reactions involving multiple reactants. Here we propose and investigate higher-order triadic percolation on hypergraphs showing that the giant component can have a non-trivial dynamics. Specifically, we demonstrate that, under suitable conditions, the order parameter of this percolation problem, i.e., the fraction of nodes in the giant component, undergoes a route to chaos in the universality class of the logistic map. In hierarchical higher-order triadic percolation, we extend this paradigm in order to treat hierarchically nested triadic interactions demonstrating the non-trivial effect of their increased combinatorial complexity on the critical phenomena and the dynamical properties of the process. Finally, we consider other generalizations of the model studying the effect of considering interdependencies and node regulation instead of hyperedge regulation.

nlin.AO↗

arXiv2024

Unveiling the Importance of Nonshortest Paths in Quantum Networks

Quantum networks (QNs) exhibit stronger connectivity than predicted by classical percolation, yet the origin of this phenomenon remains unexplored. We apply a statistical physics model -- concurrence percolation -- to uncover the origin of stronger connectivity on hierarchical scale-free networks, the ($U,V$) flowers. These networks allow full analytical control over path connectivity through two adjustable path-length parameters, $U \leq V$. This precise control enables us to determine critical exponents well beyond current simulation limits, revealing that classical and concurrence percolations, while both satisfying the hyperscaling relation, fall into distinct universality classes. This distinction arises from how they "superpose" parallel, non-shortest path contributions into overall connectivity. Concurrence percolation, unlike its classical counterpart, is sensitive to non-shortest paths and shows higher resilience to detours as these paths lengthen. This enhanced resilience is also observed in real-world hierarchical, scale-free Internet networks. Our findings highlight a crucial principle for QN design: when non-shortest paths are abundant, they notably enhance QN connectivity beyond what is achievable with classical percolation.

quant-ph↗

arXiv2023

Triadic percolation induces dynamical topological patterns in higher-order networks

Triadic interactions are higher-order interactions that occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among neuron pairs or when interneuron axon-axonic synapses enable presynaptic inhibition and facilitation, and in ecosystems when one or more species can affect the interaction among two other species. On random graphs, triadic percolation has been recently shown to turn percolation into a fully-fledged dynamical process in which the size of the giant component undergoes a route to chaos. However, in many real cases, triadic interactions are local and occur on spatially embedded networks. Here we show that triadic interactions in spatial networks induce a very complex spatio-temporal modulation of the giant component which gives rise to triadic percolation patterns with significantly different topology. We classify the observed patterns (stripes, octopus, and small clusters) with topological data analysis and we assess their information content (entropy and complexity). Moreover, we illustrate the multistability of the dynamics of the triadic percolation patterns and we provide a comprehensive phase diagram of the model. These results open new perspectives in percolation as they demonstrate that in presence of spatial triadic interactions, the giant component can acquire a time-varying topology. Hence, this work provides a theoretical framework that can be applied to model realistic scenarios in which the giant component is time-dependent as in neuroscience.

nlin.AO↗

arXiv2023

Network science Ising states of matter

Network science provides very powerful tools for extracting information from interacting data. Although recently the unsupervised detection of phases of matter using machine learning has raised significant interest, the full prediction power of network science has not yet been systematically explored in this context. Here we fill this gap by providing an in-depth statistical, combinatorial, geometrical and topological characterization of 2D Ising snapshot networks (IsingNets) extracted from Monte Carlo simulations of the $2$D Ising model at different temperatures, going across the phase transition. Our analysis reveals the complex organization properties of IsingNets in both the ferromagnetic and paramagnetic phases and demonstrates the significant deviations of the IsingNets with respect to randomized null models. In particular percolation properties of the IsingNets reflect the existence of the symmetry between configurations with opposite magnetization below the critical temperature and the very compact nature of the two emerging giant clusters revealed by our persistent homology analysis of the IsingNets. Moreover, the IsingNets display a very broad degree distribution and significant degree-degree correlations and weight-degree correlations demonstrating that they encode relevant information present in the configuration space of the $2$D Ising model. The geometrical organization of the critical IsingNets is reflected in their spectral properties deviating from the one of the null model. This work reveals the important insights that network science can bring to the characterization of phases of matter. The set of tools described hereby can be applied as well to numerical and experimental data.

cond-mat.dis-nn↗

arXiv2023

Non-parametric learning critical behavior in Ising partition functions: PCA entropy and intrinsic dimension

We provide and critically analyze a framework to learn critical behavior in classical partition functions through the application of non-parametric methods to data sets of thermal configurations. We illustrate our approach in phase transitions in 2D and 3D Ising models. First, we extend previous studies on the intrinsic dimension of 2D partition function data sets, by exploring the effect of volume in 3D Ising data. We find that as opposed to 2D systems for which this quantity has been successfully used in unsupervised characterizations of critical phenomena, in the 3D case its estimation is far more challenging. To circumvent this limitation, we then use the principal component analysis (PCA) entropy, a "Shannon entropy" of the normalized spectrum of the covariance matrix. We find a striking qualitative similarity to the thermodynamic entropy, which the PCA entropy approaches asymptotically. The latter allows us to extract -- through a conventional finite-size scaling analysis with modest lattice sizes -- the critical temperature with less than $1\%$ error for both 2D and 3D models while being computationally efficient. The PCA entropy can readily be applied to characterize correlations and critical phenomena in a huge variety of many-body problems and suggests a (direct) link between easy-to-compute quantities and entropies.

cond-mat.stat-mech↗

arXiv2022

The dynamic nature of percolation on networks with triadic interactions

Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully-fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period-doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks.

nlin.AO↗

arXiv2022

Critical time-dependent branching process modelling epidemic spreading with containment measures

During the COVID pandemic, periods of exponential growth of the disease have been mitigated by containment measures that in different occasions have resulted in a power-law growth of the number of cases. The first observation of such behaviour has been obtained from 2020 late spring data coming from China by Ziff and Ziff in Ref. [1]. After this important observation the power-law scaling (albeit with different exponents) has also been observed in other countries during periods of containment of the spread. Early interpretations of these results suggest that this phenomenon might be due to spatial effects of the spread. Here we show that temporal modulations of infectivity of individuals due to containment measures can also cause power-law growth of the number of cases over time. To this end we propose a stochastic well-mixed Susceptible-Infected-Removed (SIR) model of epidemic spreading in presence of containment measures resulting in time-dependent infectivity and we explore the statistical properties of the resulting branching process at criticality. We show that at criticality it is possible to observe power-law growth of the number of cases with exponents ranging between one and two. Our asymptotic analytical results are confirmed by extensive Monte Carlo simulations. Although these results do not exclude that spatial effects might be important in modulating the power-law growth of the number of cases at criticality, this work shows that even well-mixed populations may already feature non-trivial power-law exponents at criticality.

physics.soc-ph↗

arXiv2021

Higher-order percolation processes on multiplex hypergraphs

Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex systems and allow to investigate the relation between their higher-order structure and their function. Here we establish a general framework for assessing hypergraph robustness and we characterize the critical properties of simple and higher-order percolation processes. This general framework builds on the formulation of the random multiplex hypergraph ensemble where each layer is characterized by hyperedges of given cardinality. We reveal the relation between higher-order percolation processes in random multiplex hypergraphs, interdependent percolation of multiplex networks and K-core percolation. The structural correlations of the random multiplex hypergraphs are shown to have a significant effect on their percolation properties. The wide range of critical behaviors observed for higher-order percolation processes on multiplex hypergraphs elucidates the mechanisms responsible for the emergence of discontinuous transition and uncovers interesting critical properties which can be applied to the study of epidemic spreading and contagion processes on higher-order networks.

physics.soc-ph↗

arXiv2021

Universal nonlinear infection kernel from heterogeneous exposure on higher-order networks

The colocation of individuals in different environments is an important prerequisite for exposure to infectious diseases on a social network. Standard epidemic models fail to capture the potential complexity of this scenario by (1) neglecting the higher-order structure of contacts which typically occur through environments like workplaces, restaurants, and households; and by (2) assuming a linear relationship between the exposure to infected contacts and the risk of infection. Here, we leverage a hypergraph model to embrace the heterogeneity of environments and the heterogeneity of individual participation in these environments. We find that combining heterogeneous exposure with the concept of minimal infective dose induces a universal nonlinear relationship between infected contacts and infection risk. Under nonlinear infection kernels, conventional epidemic wisdom breaks down with the emergence of discontinuous transitions, super-exponential spread, and hysteresis.

physics.soc-ph↗

arXiv2020

A message-passing approach to epidemic tracing and mitigation with apps

With the hit of new pandemic threats, scientific frameworks are needed to understand the unfolding of the epidemic. The use of mobile apps that are able to trace contacts is of utmost importance in order to control new infected cases and contain further propagation. Here we present a theoretical approach using both percolation and message--passing techniques, to the role of contact tracing, in mitigating an epidemic wave. We show how the increase of the app adoption level raises the value of the epidemic threshold, which is eventually maximized when high-degree nodes are preferentially targeted. Analytical results are compared with extensive Monte Carlo simulations showing good agreement for both homogeneous and heterogeneous networks. These results are important to quantify the level of adoption needed for contact-tracing apps to be effective in mitigating an epidemic.

physics.soc-ph↗

arXiv2020

Renormalization group theory of percolation on pseudo-fractal simplicial and cell complexes

Simplicial complexes are gaining increasing scientific attention as they are generalized network structures that can represent the many-body interactions existing in complex systems raging from the brain to high-order social networks. Simplicial complexes are formed by simplicies, such as nodes, links, triangles and so on. Cell complexes further extend these generalized network structures as they are formed by regular polytopes such as squares, pentagons etc. Pseudo-fractal simplicial and cell complexes are a major example of generalized network structures and they can be obtained by gluing $2$-dimensional $m$-polygons ($m=2$ triangles, $m=4$ squares, $m=5$ pentagons, etc.) along their links according to a simple iterative rule. Here we investigate the interplay between the topology of pseudo-fractal simplicial and cell complexes and their dynamics by characterizing the critical properties of link percolation defined on these structures. By using the renormalization group we show that the pseudo-fractal simplicial and cell complexes have a continuous percolation threshold at $p_c=0$. When the pseudo-fractal structure is formed by polygons of the same size $m$, the transition is characterized by an exponential suppression of the order parameter $P_{\infty}$ that depends on the number of sides $m$ of the polygons forming the pseudo-fractal cell complex, i.e., $P_{\infty}\propto p\exp(-\alpha/p^{m-2})$. Here these results are also generalized to random pseudo-fractal cell-complexes formed by polygons of different number of sides $m$.

cond-mat.dis-nn↗